How do I make volumetric light fade to nothing
The issue is that your volume scattering domain is interacting with all of the other lights on the scene. To make it the less visible you could use a gradient texture node and a color ramp (as detailed in this answer), or you can do a quick trick at the expense of realism by suppresing shadow rays for on the volume scatter object and disabling volume scattering rays in the rest of the lamps. 

Select the object you are using as container for volume scattering and disable Shadow in the Ray visibility section of Cycles settings.



(also get rid of the volume absorption and add shader nodes you are using in the materials)

Then disable visibility for volume scatter for all of the other lights on the scene (so that they do not interact with the volumetric rays).



Another issue with your file is that you have a very low number of bounces for the headlights of your vehicle (Area and Area.001). In the settings for bounces bring up the value to 1024.

Lastly, know that you are going to need a lot of samples to render the image (don't rely on the denoiser, it will smudge your image)

I rendered a preview using branched path tracing using 300 AA samples and 900 for volume. But you might need more samples to get a clean image at the 8.7k render you want to do.... 



An alternative to this is not to use a mesh for volume scattering, and use volume scattering in the world and use cone lamps in the headlights instead. (all other lights still need to be disabled for Volume Scatter rays). This will give you a more natural effect, as in real life, where light beams are visible because of the suspended particles in the air. You will the shape of the beam will be more natural and it will interact better with the scene. All this at the expense of more samples and rendering time.